Futility of Bias-Free Learning

A learner that makes no a priori assumptions regarding
the identity of the target concept has no rational basis for
classifying any unseen instances.

So, what is the inductive bias?

Given an algorithm L and a set of training instances
Dc={&langle;x,c(x)&rangle;}, let L(xi,Dc) be the
classification given to xi by L after training on
Dc. The inductive bias of L is any minimal set
of assertions B for any target concept c and examples D
s.t.
∀xi&Element;XB&wedge;Dc&wedge;xi→L(xi,Dc)

For example, the inductive bias of the
Candidate-Elimination algorithm (with voting) is the
assumption that the target concept is contained in the
hypothesis space.

That is, if we make that assumption then the
classification follows logically (by
deduction).